It’s awards season, and you know what that means: overproduced costume dramas about the flaws and foibles of historical kings and queens. Or, to paraphrase the gossip weeklies, “Royals — they’re just like us!”

“A Royal Affair,” Denmark’s official submission for this year’s foreign language Oscar, is one of the stodgier entries in the parade, but it’s also one of the more straightforwardly enjoyable: a crowned-heads soap opera that balances effectively between pomp and melodramatic circumstance. In the bargain, it tells a startling real-life story of queenly bed-hopping, Enlightenment ideals, and Cabinet coups in the name of the people.

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There was a real Caroline Mathilde, a British-born queen of Denmark and Norway in the late 18th century, and she was a woman of letters who, with her court-physician lover, Johann Friedrich Struensee, coerced her mentally disturbed husband, King Christian VII, into instituting large numbers of progressive reforms. Directed by Nikolaj Arcel, “A Royal Affair” starts out in “Marie Antoinette” territory, with a blushingly naïve Caroline (Alicia Vikander) brought to the Danish countryside to meet the young royal cousin who will be her husband.

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As played by Mikkel Boe Folsgaard, King Christian is a giggling boor who prefers whores to his new queen and who occasionally drifts into furniture-smashing fits. Other than that, he’s not a bad guy. A prince is born, the marriage cools, and then the king visits Germany and brings home a new physician, the only person who can pierce his madness with friendship and understanding. The queen takes an instant dislike to this Struensee, but since he’s played by the strapping Danish matinee idol Mads Mikkelsen — US audiences know him as the Bond baddie in 2006’s “Casino Royale” — it’s only a matter of time before they’re crimping the royal linens. Oh, relax, it’s history.

“A Royal Affair” has a lot on its plate: that secret love story, the machinations at court, the war of ideas roiling Western Europe, all those gowns and castles and powdered wigs. (You know Struensee is a man of the people since he goes about with his own luxuriant mane. He’s a member of the Voltaire Hair Club for Men.) Arcel and his co-writer Rasmus Heisterberg keep the many pieces moving with duty and professionalism if not active inspiration; they know their story’s outrageous enough to carry the weight. If you have to stifle the occasional giggle when the film pivots from the queen and her lover’s discussions of Diderot and the rights of the serfs to shots of the couple galloping tempestuously across the Danish countryside — he has taught her how to ride astride rather than sidesaddle, ahem — well, such swoony interludes are part of the fun of movies.

“A Royal Affair” bogs down in the final acts, when the reactionary nobles and the church stir up the populace with pamphlets warning against “the vile German in the Queen’s chambers.” The historical particulars are enough to tide us over, though: The queen’s second child, Princess Louise Auguste, was almost certainly Struensee’s, and the two did effectively rule Denmark after convincing the king to give his physician the power of royal decree, abolishing torture and granting freedom of the press, among other novelties. For a brief, glittering moment, Denmark was the most forward-thinking country on the Continent.

In the process, King Christian becomes the most touching, if dramatically unfocused, character in the film. In Folsgaard’s interpretation, he’s unpredictable, often violent, but saved by his childlike faith in his wife and his new friend the Doctor. The two manipulate him horribly and for all the right reasons. He may be an idiot but he’s their idiot — and Denmark’s.

For her part, Vikander (who’s also in the just-released “Anna Karenina,” another Oscar-season costume party) convincingly portrays the queen’s emotional journey from wide-eyed girl to seasoned liberal politico. She weeps, she storms, she plots — she’s her people’s very own Scarlet Empress. It’s too early to say whether the star’s a great actress, but she knows where the pulpy heart of this story is, and she doesn’t lose her head. (The same can’t be said for Mikkelsen’s Struensee.) “A Royal Affair” is tosh but it’s ripely entertaining tosh, with emotions as flamboyant as the window treatments. There is nothing like a Dane.